Numerical Calculation for Phonon Properties of a Nano-Porous Si

We carried out molecular dynamics simulations (MD) of heat conduction in Si with a nano-hole to represent the nano-structure, in order to investigate the mechanism of the thermal conductivity reduction of nano-structured materials. The Stillinger-Weber potential is used in this study. The temperature is kept constant at 300K by velocity scaling. Periodic boundary conditions are applied in the x, y and z directions. Phonon dispersion curves are calculated by using the time-space 2D Fourier transform. The phonon group velocity is calculated from the slope of the dispersion curve. The velocity is reduced by nano-holes, even if those are random. Phonon mean free path can be evaluated from the width of dispersion curve, and the long waves are clearly scattered by nano-holes. Phonon density of states (DOS) is also calculated by the Fourier transform of a velocity correlation. The DOS of Si with periodic nano-holes are slightly smaller than that of a single crystal Si. In other words, the specific heat is reduced by periodic nano-holes due to the reduced phonon modes. We discuss the mechanism of the reduction of the thermal conductivity of nano-porous material on the atomic scale.